A Generalization of Resource-Bounded Measure, With an Application (Extended Abstract)

  title={A Generalization of Resource-Bounded Measure, With an Application (Extended Abstract)},
  author={Harry Buhrman and Dieter van Melkebeek and Kenneth W. Regan and D. Sivakumar and Martin Strauss},
We introduce resource-bounded betting games, and propose a generalization of Lutz's resource-bounded measure in which the choice of next string to bet on is fully adaptive. Lutz's martingales are equivalent to betting games constrained to bet on strings in lexicographic order. We show that if strong pseudo-random number generators exist, then betting games are equivalent to martingales, for measure on E and EXP. However, we construct betting games that succeed on certain classes whose Lutz… 

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